There are many different equations and ideas that are used to try and determine how common life in the universe is. Some of these conclude that life is common, and some of these conclude that we may very well be the only planet containing life in the universe. An example of one of these is the lottery comparison
The lottery comparison was made by Charles Lineweaver, an astronomer at the Australian National University (Gribbin, 31). It uses the fact that life emerged on Earth very early on after Earth’s creation. He starts with the idea that if someone buys a lottery ticket every day for three days and wins with the third ticket, we can guess that the chances of winning are good. Then, we take one person from a large group of people who bought one lottery ticket every day for 12 days and find out that he won once in one of the first three days. This means that it is likely that there is a high chance of winning.
Then, we compare this to the chance of life in our galaxy. Life starting on a planet would be considered winning the lottery and all Earth-like planets are the people that bought lottery tickets. Earth will be our sample from the group of planets (ticket purchasers). Life started on Earth very early on, which means that Earth won the lottery early on. The mathematical conclusion from this would be that life exists on approximately 13% of Earth-like planets (Gribbin, 33).